Umbrella Concepts

Complex information and vocabulary can be made more accessible by developing children’s familiarity with umbrella concepts.?I will use a square to illustrate this idea.

The umbrella concepts I will highlight in this segment are shape, number, equivalence, position, direction and measurement. These concepts relate to many other objects in the real world too, so you can apply the information below to other examples!

What’s in a Square

This is a square. This is one of the first things we teach a young child.

What is it?

A square is a universal mathematical shape which is easily recognised.

Features of a square

There are a whole lot of concepts related to a square. Read these 20 statements about a square:

·????????Each square has four corners

·????????Each square has four straight lines

·????????The lines are of equal length, two are horizontal two are vertical

·????????The lines are equilateral

·????????A square has two pairs of parallel lines

·????????Each line is perpendicular to the two lines it is connected to

·????????The lines at each corner are adjacent to each other

·????????It is a quadrangle

·????????It is quadrilateral

·????????It has four edges and four vertices

·????????Each corner is a 90-degree angle

·????????The square has an inside and an outside

·????????If we want to calculate the area, we multiply the width by the length

·????????If we bisect it from the top right-hand corner, to the bottom left-hand corner, we end up with two right-angled triangles

·????????If we bisect it from the midpoint of the top line to the midpoint of the bottom line, we get two identical rectangles

·????????A square is a kind of rectangle

·????????The square is the base of a cube prism

·????????The angles outside each corner are 270 degrees

·????????If we connect the corners with diagonal lines, the lines will intersect at the midpoint of the square

When you teach a child that the above shape is a square, do you need to give them all the other 20 pieces of information?

Of course not!

But learning about the square is the foundation for understanding the other 20 pieces of information during their later education.

If you know where their mathematical journey is headed, you can select which pieces of new information they are ready to learn and internalise. You offer the language at a level they can understand.

Many children, and even adults, will say that they are bad at maths. What has happened is that they have not internalised the meaning of the terminology. They don’t understand the relevant conceptual language.

How do you make it easier for children to learn all this language, so that they understand and use it when they need it??You arm them with umbrella concepts to help them make sense of and organise what they learn.

?Umbrella Concepts

?The 20 statements your read about a square, contain language that belongs to more manageable umbrella concepts. Let’s group some of the words together under the umbrella concepts.

Six umbrella concepts in mathematics and the questions they address

1. Shape - What form does it take?
2. Number - How many are involved?
3. Equivalence - Is it the same?
4. Position - Where is it located
5. Direction - What is the orientation?
6. Measurement -- How do we measure or quantify it?

Before you continue reading, do a quick exercise. One at a time hold the umbrella concepts in your mind and reread the statements.?Try to identify the words that belong to each umbrella concept. You might even write them down and compare them to the analysis below

Shape: square, straight, corner, angle, side, triangle, rectangle, cube, prism, base, vertex, edge

Number: a, an, the, four, each,two, pairs, prefix 'quad', 90, 270, bisect, multiply, each

Equivalence: each, equal, equilater, identical

Position: perpendicular, adjacent, edge, corner, vertex, top, right-hand, right, left-hand, left, midpoint, base,s inside, outside, intersect

Direction: straight, lateral, parallel, perpendicular, verticl, horizontal, diagonal

Measurement: length, width, area, degree

If students know what the information is about, they are more likely to remember the terminology.

There will be some words that relate to more than one concept and that is fine.

For example, ‘base’, relates to both shape and position. Some words have different meanings in mathematics than in normal life, a degree is part of a maths idea that a circle has 360 equally divided segments each called a degree; and in daily life you could earn a degree at university. Children need to be alerted to these interesting things when they learn language.

Language is the most important tool for thinking and learning and it is important to ensure that students have fully internalised the precise meaning of the words they use, so that they have mastery over them.

When children know umbrella concepts, they are more capable of understanding how the words are working together to give them specific kinds of information. You can give them practice by asking them to put pictures and later, words, into categories.

Umbrella concepts are introduced early

Giving children umbrella concepts helps them to organise their thinking and learning. You use the umbrella concept in close proximity to language which belongs to that concept, for example you use ‘shape’ alongside square; ‘position’ alongside top etc

When you teach a very young child about a square it might be enough that they

·????????identify it by appearance,

·????????say that it has corners

·????????say that the sides are straight

·????????can count the sides and corners

The expectations and language are simpler, but the umbrella concepts are already being established. There are some samples of statements in the table below about each umbrella concept for younger children. It is important that you also pay attention to number when you words like, ‘a’, ‘an’, ‘the’, ‘some’, ‘pair’, so that children are aware whether they dealing with singular or plural.

Umbrella Concept

Sample Conversation

Shape

This is a square shape. Can you see another square shape?

?A corner is a place in the shape where two lines meet. Can you point to where that happens in this shape?

This is a straight line because it doesn’t have any curves in it. Would you show your partner the straight lines?

The four lines are the four sides of the shape. Can you run your fingers along the sides of the square shape?

?In the square shape, the lines are connected at the corners. Check and see which two lines are connected at each corner?

(If the child is ready to understand ‘parallel’, this can be introduced as part of the information about the shape. This line is exactly the same distance away from this other line. Let’s test this to see if it’s true. What can we use?)

Number

The square shape has four corners and four sides. Let’s count the number of corners together. Which corner would you like to start with? Now, let’s count the number of lines. Where do you want to start?

Equivalence

Each side is the same length as the others. I wonder how we can check that they are equal? Do the corners look the same to you? Where else do you see corners.

Position

Two of the corners are in the top position and two of the corners are in the bottom position. Do you know your left from your right? Point to the corner in the top, left position. Two lines stand up, we call this a vertical position; and two lines lie down, we call this a horizontal position. Can you put your body in a vertical position, can you put it in a horizontal position?

Direction

Vertical and horizontal can describe a position or a direction. When movement is implied, they denote direction. Can you start at the bottom corner and move your finger in a vertical direction? Can you start at a bottom corner and move your finger in a horizontal direction?

Measurement

Look at the line, can you think of a way to measure how long the line is?

For degrees, you might try and have the students recognise right angles in the environment to train their eye about what perpendicular means, without introducing the words ‘degrees’ or’ perpendicular’ yet. Perpendicular is the right angle between two lines, and so they need to know a little more about angles, but they can learn to perceive what a right angle looks like experientially.

Wishing you well as you develop organised thinking by using umbrella concepts in all the subjects under the sun.

Lili-Ann Kriegler (B. A Hons, H. Dip. Ed, M.Ed.) is an education consultant and author of ‘Edu-Chameleon’. Lili-Ann’s primary specialisations are in early childhood education (birth-9 years), leadership and optimising human thinking and cognition.?Her current part-time role is as an education consultant at Independent Schools Victoria and she runs her own consultancy, Kriegler-Education. Find out more at?https://kriegler-education.com